Methods, devices and systems for enabling simultaneous operation of different technology based devices over a shared frequency spectrum

ABSTRACT

In one example embodiment, a device includes a memory configured to store computer-readable instructions therein and a processor. The processor is configured to execute the computer-readable instructions to determine a first signal of a first technology in presence of interference from at least a second signal of a second technology, the first signal and the second signal being overlappingly transmitted, the determined first signal being used for processing of information associated with the first signal.

BACKGROUND

The radio-frequency (RF) electromagnetic spectrum, extending from below1 MHz to above 100 GHz, represents a finite resource that is shared byvariety of devices including devices operating using wirelesscommunications standards, radar devices, television broadcasts, radionavigation and other RF devices. The increasing demand by consumers forhigher data rates induces competition among RF devices for accessing thefinite RF spectrum. Accordingly, appropriate federal agencies haverecently recommended that 1000 MHz of federally-controlled RF spectrumshould be freed or shared with the private industry in order to meet theever growing need for wireless communications-based services.

Radars are used for a variety of applications includingair-traffic-control, weather forecasting, automotive collision avoidancesystems, ground penetrating radars for finding underground resources,altimeters for elevation measurements, geophysical monitoring ofresources by synthetic aperture radar (SAR) systems, etc. Studies haveshown that the effect of wireless communications interference on radarsystems may severely inhibit the performance of radar devices/systems.Therefore, conventionally, when a primary device (e.g., a radar device)operates in a given spectrum (e.g., frequency band), secondary devicessuch as devices communicating using wireless communicationstechnologies, have not been allowed to operate in the given spectrum.

Various solutions have been proposed for enabling the use of “whitespectrum” (e.g., RF spectrum used by primary devices) by the secondarydevices. This means allowing secondary wireless devices to operate whenthe primary wireless device(s) are not active within a frequency bandand geographical area. One such proposed solution is referred to asDynamic Spectrum Access (DSA), with Dynamic Frequency Selection (DFS)being a particular example of the DSA solution.

Another proposed solution (not currently implemented or not implementedfor spectrum sharing purposes) might be radar systems such as passivesystems and multiple-input multiple-output (MIMO) radars to alleviatethe spectrum congestion problem and make more spectrum available for useby wireless communications systems. However these systems are much morecomplex than the existing deployed radar systems. Furthermore,replacements of existing radar systems may be cost prohibitive andconsequently such proposed systems are not currently feasible.

Therefore, more robust methods allowing for simultaneous operation ofwireless communications and radar devices/systems are desirable.

SUMMARY

Some example embodiments relate to methods, apparatuses and systems forenabling simultaneous operation of different technology based devicesover a shared spectrum.

In one example embodiment, a device includes a memory configured tostore computer-readable instructions therein and a processor. Theprocessor is configured to execute the computer-readable instructions todetermine a first signal of a first technology in presence ofinterference from at least a second signal of a second technology, thefirst signal and the second signal being overlappingly transmitted, thedetermined first signal being used for processing of informationassociated with the first signal.

In yet another example embodiment, the overlapping transmission of thefirst signal and the second signal includes transmission of the firstsignal and the second signal over a shared spectrum.

In yet another example embodiment, the overlapping transmission of thefirst signal and the second signal includes transmission of the firstsignal and the second signal over a shared spectrum.

In yet another example embodiment, the overlapping transmission of thefirst signal and the second signal includes a spatial overlap of thefirst signal and the second signal as well as overlaps of the firstsignal and the second signal in time and frequency domains.

In yet another example embodiment, the processor is further configuredto receive a signal, the signal including the first signal with additivenoise corresponding to at least the second signal, and minimize a costfunction associated with the received signal, wherein the processor isconfigured to determine the first signal as possible sets of values ofthe first signal that minimize the cost function.

In yet another example embodiment, the processor is further configuredto minimize the cost the function based on an iterative process.

In yet another example embodiment, the first signal is a radarfast-time/slow-time data matrix, and the cost function is formed basedon at least the received signal, a range-frequency spectrum associatedwith a transmission of the first signal, a set of Doppler weights, atleast one regularization function, at least one data-fidelity term, atleast one regularization parameter, a step-size parameter and a powerspectral density of the second signal.

In yet another example embodiment, the first signal is a radar datatime-series, and the cost function is formed based on at least thereceived signal, a frequency response of a filter associated with atransmission of the first signal, a regularization parameter, at leastone regularization function, at least one data-fidelity term, at leastone regularization parameter, a step-size parameter and a power spectraldensity of the second signal.

In yet another example embodiment, the device is a receiver of a radarsystem, the first signal is a radar signal transmitted by a transmitterof the radar system, the second signal is a signal transmitted by atransmitter of a wireless communications system, the radar systemoperates based on the first technology, and the wireless communicationssystem operates based on the second technology.

In yet another example embodiment, the first technology is a radartechnology, and the second technology is a wireless communicationsstandard, the wireless communications standard being at least one of awireless local area networking standard and a radio access technology.

In yet another example embodiment, the radar system is configured tooperate simultaneously with at least one additional radar system, andthe processor is further configured to suppress radar signals of theleast one additional radar system, when the processor determines thefirst signal.

In yet another example embodiment, the processor is further configuredto suppress the radar signals of the least one additional radar systemby adjusting power spectral densities in a cost function on frequencieson which the radar signals of the least one additional radar system aretransmitted.

In one example embodiment, a device includes a memory configured tostore computer-readable instructions therein and a processor. Theprocessor is configured to determine a first signal of a firsttechnology from a signal received at the device, the signal including atleast the first signal and a second signal of a second technologytransmitted for reception by the device. The processor is furtherconfigured to determine the second signal based on the signal and thefirst signal, the determined second signal being used for processing ofinformation associated with the second signal.

In yet another example embodiment, the overlapping transmission of thefirst signal and the second signal includes transmission of the firstsignal and the second signal over a shared spectrum.

In yet another example embodiment, the overlapping transmission of thefirst signal and the second signal includes a spatial overlap of thefirst signal and the second signal as well as overlaps of the firstsignal and the second signal in time and frequency domains.

In yet another example embodiment, the processor is further configuredto receive the signal, the signal including the first signal withadditive noise corresponding to at least the second signal, and minimizea cost function associated with the received signal, wherein theprocessor is configured to determine the first signal as possible valuesof the first signal that minimize the cost function.

In yet another example embodiment, the processor is further configuredto minimize the cost function based on an iterative process.

In yet another example embodiment, the first signal is a radarfast-time/slow-time data matrix, and the cost function is formed basedon at least the received signal, a range-frequency spectrum associatedwith a transmission of the first signal, a set of Doppler weights, atleast one regularization function, at least one data-fidelity term, atleast one regularization parameter, a step-size parameter and a powerspectral density of the second signal.

In yet another example embodiment, the first signal is a radar datatime-series, and the cost function is formed based on at least thereceived signal, a frequency response of a filter associated with atransmission of the first signal, a regularization parameter, at leastone regularization function, at least one data-fidelity term, at leastone regularization parameter a step-size parameter and a power spectraldensity of the second signal.

In yet another example embodiment, the device is a receiver of awireless communications system, the first signal is a radar signaltransmitted by a transmitter of a radar system, the second signal is asignal transmitted by a transmitter of the wireless communicationssystem, the radar system operates based on the first technology, and thewireless communications system operates based on the second technology.

In yet another example embodiment, the first technology is a radartechnology, and the second technology is a wireless communicationsstandard, the wireless communications standard being at least one of awireless local area networking standard and a radio access technology.

In yet another example embodiment, the processor is further configuredto receive the signal, the signal including the first signal, the secondsignal and at least one additional radar signal, determine the firstsignal and the at least one additional radar signal, and subtract acombination of the first signal and the at least one additional radarsignal from the signal to determine the second signal.

In yet another example embodiment, the wireless communications system isconfigured to operate simultaneously with at least one additionalwireless communications system, and the processor is further configuredto suppress wireless communications signals of the least one additionalwireless communications system, when the processor determines the secondsignal.

BRIEF DESCRIPTION OF THE DRAWINGS

Example embodiments will become more fully understood from the detaileddescription given herein below and the accompanying drawings, whereinlike elements are represented by like reference numerals, which aregiven by way of illustration only and thus are not limiting of thepresent disclosure, and wherein:

FIG. 1 illustrates a setting in which a wireless communications systemand a radar system operate simultaneously, according to an exampleembodiment;

FIG. 2 illustrates a setting in which a wireless communications systemand a moving radar system operate simultaneously, according to anexample embodiment;

FIG. 3 illustrates a receiver for receiving signals of the first systemshown in FIG. 1, according to an example embodiment;

FIG. 4 illustrates a receiver for receiving signals of the second systemshown in FIG. 1, according to an example embodiment;

FIG. 5 is a flowchart describing a method of determining a signal inpresence of interference induced by an overlappingly transmitted signalof a different technology, according to an example embodiment; and

FIG. 6 is a flowchart describing a method of determining a signal inpresence of interference induced by an overlappingly transmitted signalof a different technology, according to an example embodiment.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

Various embodiments will now be described more fully with reference tothe accompanying drawings. Like elements on the drawings are labeled bylike reference numerals.

Detailed illustrative embodiments are disclosed herein. However,specific structural and functional details disclosed herein are merelyrepresentative for purposes of describing example embodiments. Thisdisclosure may, however, be embodied in many alternate forms and shouldnot be construed as limited to only the embodiments set forth herein.

Accordingly, while example embodiments are capable of variousmodifications and alternative forms, the embodiments are shown by way ofexample in the drawings and will be described herein in detail. Itshould be understood, however, that there is no intent to limit exampleembodiments to the particular forms disclosed. On the contrary, exampleembodiments are to cover all modifications, equivalents, andalternatives falling within the scope of this disclosure. Like numbersrefer to like elements throughout the description of the figures.

Although the terms first, second, etc. may be used herein to describevarious elements, these elements should not be limited by these terms.These terms are only used to distinguish one element from another. Forexample, a first element could be termed a second element, andsimilarly, a second element could be termed a first element, withoutdeparting from the scope of this disclosure. As used herein, the term“and/or,” includes any and all combinations of one or more of theassociated listed items.

When an element is referred to as being “connected,” or “coupled,” toanother element, it can be directly connected or coupled to the otherelement or intervening elements may be present. By contrast, when anelement is referred to as being “directly connected,” or “directlycoupled,” to another element, there are no intervening elements present.Other words used to describe the relationship between elements should beinterpreted in a like fashion (e.g., “between,” versus “directlybetween,” “adjacent,” versus “directly adjacent,” etc.).

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting. As used herein, thesingular forms “a”, “an”, and “the” are intended to include the pluralforms as well, unless the context clearly indicates otherwise. It willbe further understood that the terms “comprises”, “comprising,”,“includes” and/or “including”, when used herein, specify the presence ofstated features, steps, operations, elements, and/or components, but donot preclude the presence or addition of one or more other features,integers, steps, operations, elements, components, and/or groupsthereof.

It should also be noted that in some alternative implementations, thefunctions/acts noted may occur out of the order noted in the figures.For example, two figures shown in succession may in fact be executedsubstantially concurrently or may sometimes be executed in the reverseorder, depending upon the functionality/acts involved.

Specific details are provided in the following description to provide athorough understanding of example embodiments. However, it will beunderstood by one of ordinary skill in the art that example embodimentsmay be practiced without these specific details. For example, systemsmay be shown in block diagrams so as not to obscure the exampleembodiments in unnecessary detail. In other instances, well-knownprocesses, structures and techniques may be shown without unnecessarydetail in order to avoid obscuring example embodiments.

In the following description, illustrative embodiments will be describedwith reference to acts and symbolic representations of operations (e.g.,in the form of flow charts, flow diagrams, data flow diagrams, structurediagrams, block diagrams, etc.) that may be implemented as programmodules or functional processes include routines, programs, objects,components, data structures, etc., that perform particular tasks orimplement particular abstract data types and may be implemented usingexisting hardware at existing network elements. Such existing hardwaremay include, but is not limited to, one or more of Central ProcessingUnits (CPUs), Digital Signal Processors (DSPs), Graphical ProcessingUnits (GPUs), Very Large Scale Integration (VLSI) circuits,Application-Specific-Integrated-Circuits (ASICs), Field ProgrammableGate Arrays (FPGAs), computers or the like.

Although a flow chart may describe the operations as a sequentialprocess, many of the operations may be performed in parallel,concurrently or simultaneously. In addition, the order of the operationsmay be re-arranged. A process may be terminated when its operations arecompleted, but may also have additional steps not included in thefigure. A process may correspond to a method, function, procedure,subroutine, subprogram, etc. When a process corresponds to a function,its termination may correspond to a return of the function to thecalling function or the main function.

As disclosed herein, the term “storage medium” or “computer readablestorage medium” may represent one or more devices for storing data,including read only memory (ROM), random access memory (RAM), magneticRAM, core memory, magnetic disk storage mediums, optical storagemediums, flash memory devices and/or other tangible machine readablemediums for storing information. The term “computer-readable medium” mayinclude, but is not limited to, portable or fixed storage devices,optical storage devices, and various other mediums capable of storing,containing or carrying instruction(s) and/or data.

Furthermore, example embodiments may be implemented by hardware,software, firmware, middleware, microcode, hardware descriptionlanguages, or any combination thereof. When implemented in software,firmware, middleware, or microcode, the program code or code segments toperform the necessary tasks may be stored in a machine or computerreadable medium such as a computer readable storage medium. Whenimplemented in software, a processor or processors will perform thenecessary tasks.

A code segment may represent a procedure, function, subprogram, program,routine, subroutine, module, software package, class, or any combinationof instructions, data structures or program statements. A code segmentmay be coupled to another code segment or a hardware circuit by passingand/or receiving information, data, arguments, parameters or memorycontent. Information, arguments, parameters, data, etc. may be passed,forwarded, or transmitted via any suitable means including memorysharing, message passing, token passing, network transmission, etc.

Example embodiments described herein enable simultaneous operation ofdevices/systems of different technologies over a shared frequencyspectrum while detrimental interference of signals of one of thedifferent technologies on signals of another one of the differenttechnologies is minimized.

Example embodiments described herein provide a signal processingapproach, in which a first device of a first technologydetermines/estimates a signal transmitted according to the firsttechnology and destined for the first device, from a mixed signalreceived at the first device. The mixed signal includes, among varioustypes of interference signals, a signal simultaneously transmittedaccording to a second technology over the same frequency spectrum (thefirst and second signals overlap in time and frequency domains). Thefirst device may then utilize the determined/estimated first signal forfurther processing of information associated with the first signal.

Example embodiments may be utilized in conjunction with various known orto be developed Wireless Local Area Network Technologies (WLANs).Furthermore, example embodiments may also be utilized in conjunctionwith Radio Access Networks (RANs) such as: Universal MobileTelecommunications System (UMTS); Global System for Mobilecommunications (GSM); Advance Mobile Phone Service (AMPS) system; theNarrowband AMPS system (NAMPS); the Total Access Communications System(TACS); the Personal Digital Cellular (PDC) system; the United StatesDigital Cellular (USDC) system; the code division multiple access (CDMA)system described in EIA/TIA IS-95; a High Rate Packet Data (HRPD)system, Worldwide Interoperability for Microwave Access (WiMAX); 4G LongTerm Evolution (LTE); Wi-Fi; Ultra Mobile Broadband (UMB); and 3^(rd)Generation Partnership Project LTE (3GPP LTE).

FIG. 1 illustrates a setting in which a wireless communications systemand a radar system operate simultaneously, according to an exampleembodiment. As shown in FIG. 1, in a setting 100 two different systemsco-exist. The first system is the system 120 and the second system isthe system 130. The systems 120 and 130 may operate based on differenttechnologies. In the example embodiment shown in FIG. 1, the system 120may be a radar system and the system 130 may be a wirelesscommunications system. However, example embodiments are not limited towireless communications and radar systems but may encompass any twosystems operating according to different technologies. For purposes ofdescribing example embodiments, the first system 120 and the secondsystem 130 are considered to exist in vicinity of one another or havingspatially overlapping signals (i.e., the first system 120 and the secondsystem 130 overlap spatially such that when the first system 120 and thesecond 130 transmit signals on the same or overlapping frequencies andsame or overlapping time, the signals of each induce interference on thesignals of the other of the two systems (each of the first system 120and the second system 130 experience degradation in their performancedue to the spatial overlap of the signals (e.g. in the radiatedelectromagnetic waves form) of the other of the two systems.)

The first system 120 may be a system that operates based on a differenttechnology than the technology based on which the second system 130operates. For example and as shown in FIG. 1, the first system 120 maybe a radar system. The radar system 120 may include a radar receiver122, a radar 124, and a radar object of detection 126. The radarreceiver 122 may control the operation of the radar 124, as will bedescribed below. The radar 124 may transmit a signal 128 to the radarobject of detection 126. The echo/reflection of the signal 128 may bethe signal 129 received back/detected by the radar 124 and processed bythe radar receiver 122. The radar object of detection may be any type ofobject/information to be detected, imaged, tracked, processed, and/ormonitored by the radar 124.

The radar system 120 may be any coherent based radar system such as aweather radar system, surveillance radar system, airport traffic radarsystem, ground penetrating radar system, search and rescue radar system,car radar system including those with multiple array elements andmultiple antennas (MIMO). The radar may be in a staring mode, scanningmode, circling mode, stripmap mode, etc. The radar may also be in anyone of an imaging, tracking, detection or other modes.

The second system 130 may include components necessary for enablingcommunication according to the corresponding technology. For example, inFIG. 1 and assuming that the second system 130 operates according to awireless communications technology (e.g., GSM based wirelesscommunications system, CDMA based communications system, etc.), thesecond system 130 may include a wireless access point 132 communicatingwith communication client devices 134 (which may be hereinafter referredto as user equipment (UE)) via exchange of signals 136. The Wirelessaccess point 132 may differ from one wireless communications technologyto another but regardless of the underlying technology, enables the UEs134 to establish voice/data communication with other devices and/ornetwork components.

In one example embodiment and as shown in FIG. 1, the wireless accesspoint 132 may be a base station (e.g., macro cell base station, smallcell base station, femto cell base station, etc.). However, the exampleembodiments are not limited thereto but may encompass any other type ofaccess point through which the UEs 134 may establish voice/datacommunications with other UEs (in the same network or differentnetworks) or other network components. For example, the wireless accesspoint 132 may be a router, when the wireless communications system 130is a wireless local area network (WLAN) operating according to knownWLAN standards such as IEEE 802 standards. Furthermore, while somecomponents of the second system 130 are illustrated in FIG. 1, any othercomponent necessary for enabling wireless communication within thesecond system 130 is implicitly included (e.g., network access points,core network elements, etc.).

More generally, the first system 120 and the second system 130 may besystems of sensors and/or system of communication devices using the samespectrum resources where the waveforms may be electromagnetic, acousticor otherwise. The wireless communications and radar platforms may bestationary or moving on the ground, in the air/space or at the sea.

The radar system 120 may operate in one or more frequency bands (e.g., 5GHz band).

In one example embodiment, the signals 136 of the wirelesscommunications system 130 and the signals 128/129 of the radar system120 may be transmitted simultaneously over the same (or overlapping)frequency band/spectrum such that the signals 136 and 128/129 overlap intime and/or frequency domains (i.e., the signals 136 and 128/129 may besaid to share a spectrum, with the shared spectrum being associated withone or more specific frequencies such as 2 GHz, 5 GHz, etc.). Forexample, signals 136 and 128/129 may be transmitted over the entireand/or overlapping portions of the 5 GHz frequency band. Accordingly,the signals of each of the systems 120 and 130 (e.g., signals 136, 128and 129) may induce interference on signals of the other one of thesystems 120 and 130. The interference caused by each of the signals 136and 128/129 on the other one of the signals 136 and 128/129 isillustrated as interference signals 140 in FIG. 1.

For example, the signals 136 of the system 130 may interfere with thetransmitted and received signals 128/129 of the system 120. Accordingly,the signal 129, as received at the radar receiver 122 may include boththe intended signal 129 as well as the interference induced/caused bythe signal 136 of the system 130, in the form of signal 140. Similarly,the signals 128/129 of the system 120 may interfere with the signals 136of the system 130. Accordingly, the signal 136, as received at areceiver of any one or more of the components in the system 130 (e.g., areceiver of any one of the UEs 134 and/or the wireless access point 132)may include the signal 136 as well as the interference induced/caused bythe signals 128/129 of the system 120, in the form of signal 140.Accordingly, and as will be described in greater detail below, exampleembodiments enable a receiver in each of the systems 120 and 130 todetermine/estimate the corresponding one of the signals 136 or 129 fromthe mixture of the corresponding one of the signals 136 or 129 and theinterference induced at least in part by the interference signals 140 ofthe other one of the systems 120 and 130.

While FIG. 1 illustrates a setting in which only two systems (system 120and system 130) operating according to different technologies aredeployed, example embodiments are not limited thereto. For example,there may be a more than two systems deployed in the setting 100 each ofwhich operates based on a different technology and/or any pair of two ormore of the deployed systems may operate based on the same technologywhile at least one of the deployed system operates based on a differenttechnology. Regardless of the number of systems in the setting 100, eachsystem's transmitted signals may induce interference such asinterference signal 140 on the other systems in the setting 100.

FIG. 2 illustrates a setting in which a wireless communications systemand a moving system operate simultaneously, according to an exampleembodiment. As shown in FIG. 2, in a setting 200 two different systemsco-exist (i.e., physically co-exist meaning that the two systems (and/oralternatively the signals transmitted by the two systems) are in thegeographical vicinity of one another). The first system is a radarsystem formed by the radar 201 and the radar objects of interest 203,similar to the system 120 shown in FIG. 1, except that in FIG. 2, theradar 201 moves (electronically, mechanically, manually, etc.) along thedirection 207. The moving radar system may be ship-born, airborne,satellite or moving on land. The movement of the radar 201 is shown bythree different radar 201 s each illustrating a different position ofthe radar 201 at a different location along the line/axis 207. In oneexample embodiment, the radar 201 may be positioned on a movableplatform enabling the radar 201 to be moved to different locations. Thesystems shown in FIG. 2 may operate based on different technologiesincluding wireless communications and radar systems, as also describedabove with reference to FIG. 1. However, example embodiments are notlimited to wireless communications and radar systems but may encompassany two systems operating according to different technologies.

The second system in FIG. 2 is the system comprising the wireless accesspoint 205 and the communication client device 206 (which may also bereferred to as the user equipment (UE) 206), similar to the system 130shown in FIG. 1. While not shown and as also described above, the secondsystem in FIG. 2 may include any other number of system components inaccordance with the technology based on which the second systemoperates.

In FIG. 2, at the different locations, the radar 201 may observe a radarscene 204 for detecting (and/or imaging, tracking, monitoring, etc.,depending on the functionality of the radar system) one or more of theradar objects 203. The radar objects 203 may be located in the vicinityof the second system of which the wireless access point 205 and the UE206 are part of. Accordingly, the signals of the two systems, which aretransmitted overlappingly over a shared frequency spectrum/bandwidth(the shared spectrum associated with one or more particularfrequencies), may interfere with one another when a radar footprint 204formed by the main beam (or sidelobe or backlobe) 202 of the radar 201overlaps the radiated energy from the wireless communications systemformed by the wireless access point 205 and the UE 206. In one exampleembodiment, the signals of the two systems may interfere in time andfrequency domains either completely or partially.

FIG. 3 illustrates a receiver for receiving signals of the first systemshown in FIG. 1, according to an example embodiment. In the exampleembodiment described above with reference to FIG. 1, the first system120 is described as a radar system. However, as mentioned, the firstsystem 120 is not limited to a radar system.

The receiver of FIG. 3 may be the radar receiver 122 of the first system120 of FIG. 1 that is to receive an echo from the radar signaltransmitted by the radar 124 to the radar object of detection 126 andreflected back to the radar 124 from the radar object of detection 126.

As shown in FIG. 3, the radar receiver 122 may include a storage mediumdevice 345 and a processor 350. While FIG. 3 illustrates the radarreceiver 122 as including two components, example embodiments are notlimited thereto and the radar receiver 122 may include any number ofadditional components necessary for performing various functions withinthe radar system 120.

The storage medium device 345 may store, among other information, a setof computer-readable instructions and parameters for determining asignal of the first system 120 transmitted to the radar receiver 122 inpresence of interference induced by the signal 140 described above withreference to FIG. 1, as will be described below.

The processor 350 may execute the set of computer-readable instructionsfor performing the functions necessary to determine a signal of thefirst system 120 transmitted to the radar receiver 122, as will bedescribed below. Accordingly, the execution of the computer-readableinstructions by the processor 350 may transform the processor 350 into aspecial purpose processor for performing the underlying functions. Inaddition to determining the signal of the first system 120, theprocessor 350 may further execute additional computer-readableinstructions for processing information associated with the receivedsignal, as will be further described below.

FIG. 4 illustrates a receiver for receiving signals of the second systemshown in FIG. 1, according to an example embodiment. In the exampleembodiment described above with reference to FIG. 1, the second system130 is described as a wireless communications system. However, asmentioned, the second system 130 is not limited to a wirelesscommunications system.

The receiver 450 shown in FIG. 4 may be a receiver at any one of thecomponents in the second system 130 of FIG. 1 that is to receive asignal transmitted according to the technology based on which the secondsystem 130 operates. For example, the receiver 450 shown in FIG. 3 maybe a receiver at the UE 134, a receiver at the wireless access node 132or a receiver at any other network component within the second system130.

As shown in FIG. 4, the receiver 450 may include a storage medium device455, a processor 460 and an antenna 465. While FIG. 4 illustrates thereceiver 450 as including three components, example embodiments are notlimited thereto and the receiver 450 may include any number ofadditional components necessary for performing various functions withinthe second system 130.

The storage medium device 455 may store, among other information, a setof computer-readable instructions and parameters for determining asignal of the second system 130 transmitted to the receiver 450, as willbe described below.

The processor 460 may execute the set of computer-readable instructionsfor performing the functions necessary to determine a signal of thesecond system 130 transmitted to the receiver 450, as will be describedbelow. Accordingly, the execution of the computer-readable instructionsby the processor 460 may transform the processor 460 into a specialpurpose processor for performing the underlying functions. In additionto determining the signal of the second system 130 in presence ofinterference signal 140 described above with reference to FIG. 1, theprocessor 450 may further execute additional computer-readableinstructions for processing information associated with the receivedsignal, as will be further described below.

The antenna 465 may be any known or to be developed antennainstalled/incorporated into the receiver 450 (which may vary dependingon the component of the second system 130 in which the receiver 450 isembedded). The antenna 465 may be used to receive signals (which may bea mixture of the signal of the second system 130 as well as interferenceinduced by an overlappingly transmitted signal of the first system 120(in the form of interference signal 140 discussed above with referenceto FIG. 1, as well as additional noise interference)). The antenna 465may additionally be used to transmit data/information/signals to othercomponents of the second system 130 (e.g., the antenna 465 may be atransceiver antenna).

Prior to describing example embodiments directed todetermining/estimating a particular signal from mixed signal received ata receiver (the mixed signal including an overlappingly transmittedsignal of a different technology), several definitions and conditionsfor doing so are defined first.

As mentioned above, example embodiments provide spectrum sharingalgorithms between systems operating based on different technologies(e.g., wireless communications and radar technologies). For example, thespectrum sharing algorithms enable determining a corresponding signal byone of the different systems in presence of interference fromoverlappingly transmitted signals of other systems, as Fast Transforms(such as Fast Fourier Transform (FFT)-based, Discrete Cosine Transform(DCT)-based, Wavelet-based) iterative solutions to an optimization costfunction. Example embodiments of spectrum sharing methods describedherein may be applied by each of the different systems (i.e., may beimplemented at a receiver in each of the different systems) without anyprior communications between the different systems. However, in someexample embodiment, minimal amount of priori information may also beshared among components of the different systems.

Hereinafter, example embodiments will be described with respect to radarand wireless communications systems as specific examples of thedifferent technology-based systems (e.g., systems 120 and 130 of FIG. 1,described above) that may co-exist and overlap in spectrum fortransmission of signals. However as indicated, the first and secondsystems 120 and 130 may be any two systems operating based on differenttechnologies.

In example embodiments described hereinafter, a radar system (i.e., thefirst system 120 described above with reference to FIG. 1) is assumed totransmit a periodic series of pulses where the interval between eachsuccessive pulse is denoted as T. Furthermore, a pulse repetitioninterval (PRI) is defined as the interval between each successive pulsewith the inverse thereof being denoted as the pulse repetition frequency(PRF). The PRF may be given by f_(r)=1/T. In such pulse radar system, amodulated pulsed waveform p(t) with a bandwidth B_(p) may be transmittedevery T seconds. In particular, p(t) may be a frequency, phase oramplitude modulated waveform or a combination thereof. For example, inmany currently deployed radar systems, p(t) is a linear frequencymodulated chirp signal. However, example embodiments described hereinare applicable to other types of sampled transmittable waveforms.Furthermore, the example embodiments are not limited to periodicallypulsed radars and may encompass non-periodically pulsed radars as wellas continuous wave radars.

In order to propagate in the RF environment, p(t) may be up-converted toan appropriate carrier frequency before transmission thereof by a radar(e.g., the radar 124 shown in FIG. 1). Furthermore, the radar 124 maytransmit a total of M (with M being a positive integer) pulses in acoherent pulse interval (CPI). The radar 124 may receive echoes from theM pulses, which may then be down-converted and sampled at a rate B_(h)and stored in a data matrix y(m,l) by the radar receiver 122, where mdenotes the m^(th) pulse in a CPI and l indexes the range-cell returndata. In one example embodiment, the data matrix y(m,l) may denote boththe pulse/range matrix obtained prior to pulse compression or afterpulse compression. Furthermore, the data matrix may be taken as adigital dataset after sampling of the returns of each PRI. Such datamatrix, as is known in the art, may also be referred to as aslow-time/fast-time data matrix. Accordingly, the index l may denote therange-samples or fast-time data with the awareness that l is index forthe scattered return of each PRI, and the index m may denote thepulse-samples or slow-time data.

In one example embodiment, B_(h), which is the sampling rate used toobtain the fast-time data, is greater than the Nyquist bandwidth of p(t)for some signal processing tasks such as filtering. Furthermore, thereceived signal in the range dimension may be modeled as a linearconvolution of the range reflectivity function and the modulated radartransmit pulse p(t). After demodulation of the echoes received fromtarget objects (e.g., radar object of detection 126) and sampling, eachrow of the data matrix y(m,l) may represent a linear convolution of awaveform filter with the radar reflectivity of the scene. The term“scene” may refer to the radar object of detection 126, as shown in FIG.1 and/or an area that is an antenna footprint such as the area 204 inFIG. 2.

In one example embodiment, the linear convolution represented by eachrow of the data matrix y(m,l) may be transformed into a circularconvolution by appropriate zero-padding of a waveform filter and acomplex baseband reflectivity. The waveform filter may be the transmitfilter which generates the transmit pulse. Alternatively, the waveformfilter may be the transmit filter convolved with the receiver transferfunction response. The complex baseband reflectivity represents thereflectivity of the scene.

In addition to the scattered return PRI, the data matrix y(m,l) may alsoinclude additive system noise, where an overlappingly transmitted signalof another co-existing system (e.g., the wireless communications system)is part of the additive noise. Accordingly, the data matrix y(m, l) mayalso be referred to as the noisy data matrix y(m, l). The noisy datamatrix y(m, l) may be written as:

y=h* _(r) x+w  (1)

x,y,w ε

^(N) ^(d) ^(×N) ^(r) ,hε

^(N) ^(r)   (2)

where the operation *_(r) is the circular convolution operationperformed on each row of the data matrix y(m, l), as shown in Equation(3) below.

y=h* _(r) x

y(m,l)=Σ_(k) h(k)x(m,

l−k

_(N) _(r) )  (3)

In Equation (1) above, w is composed of two components w_(n) and w_(i).The component w_(n) denotes an additive system noise term which may beconsidered as white noise. The component w_(i) represents interferenceinduced by other devices (e.g., due to the interference signal 140 shownin FIG. 1). In general, w may be a colored noise process. Furthermore,in Equation (1) x is the complex baseband reflectivity of the radarscene with row dimension size of M, which is, as described above, thenumber of slow-time pulses. Moreover, in Equation (1) h, which is thewaveform filter, is the sampled discrete signal obtained from samplingtransmit pulse p(t) that has been through the receiver at the rate ofB_(h). One objective of example embodiments described herein, is todetermine/estimate x from the received signal/data matrix y.

In one example embodiment and based on Equation (1), the sampleddiscrete signal h and each row of complex baseband reflectivity x arezero-padded to a length N_(r), so that the linear convolution betweenthe discrete signal h and any row of the complex reflectivity may beexpressed as a circular convolution operation *_(r) defined above inEquation (3). Similarly, each column in the data-matrix is zero-paddedappropriately to a size N_(d) (In one example embodiment, N_(d) isgreater than the number of pulses in a CPI) so that Doppler MTIfiltering may be performed in the frequency domain without anywrap-around effects.

In example embodiment, the Fourier transform for Doppler and range,which is implemented as the FFT solution to an optimization problem, isused. The Fourier transform for Doppler is denoted as F_(D) and theFourier transform for range is denoted as F_(R). The range Fouriertransform F_(R) is set to be a unitary transform, i.e., such that

F _(R) ^(H) F _(R) =I,F _(R) F _(R) ^(H) =I  (4a)

where F^(H) denotes the complex conjugate transpose of F and I is theidentity matrix with diagonal elements being equal to 1 and theremaining element being equal to zero.

The Doppler Fourier transform F_(D) may be set to be an overcompleteParseval transform, i.e., such that

F _(D) ^(H) F _(D) =I,F _(D) F _(D) ^(H) ≠I  (4b)

Where the operator F_(D) is ‘tall’ and F_(D) ^(H) is ‘wide’, as is knownin the art. F^(H) and I are as described above with reference toEquations (4a). While F_(D) has been described as an overcompletetransform in one example embodiment, example embodiments are not limitedthereto. In example embodiments F_(D), may be an undercomplete transformor a complete transform.

In one example embodiment, the range Fourier transform is applied alongthe rows of the data matrix y while the Doppler Fourier transform isapplied on each individual column of the data matrix y. Because therange and Doppler Fourier transforms are applied along separatedimensions of a data matrix y, the range and Doppler Fourier transformsare said to commute. Accordingly, the range Fourier transform of theconvolution of the sampled discrete signal h and the basebandreflectivity x is given by:

F _(R)(h* _(r) x)=√{square root over (N _(r))}(H⊙ _(R) X)  (5)

Where ⊙_(R) is a point-wise multiplication and H and X are defined asthe range Fourier transform of h and x. Furthermore, h and H are onedimensional vectors while x and X are two dimensional vectors (i.e., amatrix). In order for point-wise multiplication to be defined between Hand X, the one dimensional vector H must be expanded to a twodimensional vector. Therefore, the operator ⊙_(R) is defined to expand Hso as to have an equal number of rows as X, i.e.,

Y=H⊙ _(R) X

Y(m,k)=H(k)X(m,k)  (6)

where m is as defined above and k is an index in the range-frequencydomain (which corresponds to the radio-frequency domain).

In operator notation, ⊙_(R) may be defined as:

H⊙ _(R) X=rpm(H)X  (7)

where rpm(H) is defined as ‘range point-wise multiplication’ and denotesthe diagonal operator defined by (7), i.e.:

[rpm(H)X] _(m,k) =H(k)X(m,k)  (8)

By applying Equation (7) to Equation (5), the following identity isobtained:

F _(R)(h* _(r) ,x)=√{square root over (N _(r))} rpm(H)X  (9)

Given the commuting property of the Doppler Fourier transform and rangeFourier transform, as described above, the following identities may beestablished:

rpm(H)F _(D) =F _(D)rpm(H)  (10)

rpm(H)F _(D) ^(H) =F _(D) ^(H) rpm(H)  (11)

The energy metric, and the l₂ and l₁ norms of x may be writtenrespectively as:

$\begin{matrix}{{{x}_{2}^{2} = {\sum\limits_{m}{\sum\limits_{k}{{x\left( {m,k} \right)}}^{2}}}},{{x}_{2} = \sqrt{\sum\limits_{m}{\sum\limits_{k}{{x\left( {m,k} \right)}}}}},{{x}_{1} = {\sum\limits_{m}{\sum\limits_{k}{{x\left( {m,k} \right)}}}}}} & (12)\end{matrix}$

where the two-norm applied element-wise on the elements of a matrix xmay also be referred to as the Frobenius norm.

Using the Parseval's property known in the art, the l₂ norm of x may bewritten as:

∥x∥ ₂ =∥F _(D) x∥ ₂ =∥F _(R) x∥ ₂  (13)

In example embodiments described herein, x may also be considered theinverse Fourier transform of the range-Doppler profile of the inputscene (e.g., the first signal to be determined/estimated from thereceived signal y), denoted by s:

x=F _(D) ^(H) S  (14)

where each row of s represents one Doppler Frequency and each column ofs represents one range cell.

Accordingly, one objective of example embodiments described herein is todetermine/estimate s when there is simultaneous transmission of signalsby systems operating based on different technologies (e.g., signalstransmitted by a wireless communications system and a radar system,described above with reference to FIG. 1).

Example embodiments for determining/estimating s include minimizing aninverse problem (e.g. minimize a cost function) with an appropriate datafidelity term, regularization term and an estimated noise statistics(the noise including the corresponding system noise w_(n) as well asnoise w_(i) induced by an interfering and overlappingly transmittedsignal of another system operating based on a different technology, asdescribed above) such as the power spectral density of the noise.Accordingly, in order to determine/estimate s, a proper cost functionmay be formulated. The cost function may include, among other terms, adata fidelity term, a regularization term and an estimation of the noisestatistics. Therefore, prior to describing example embodiments fordetermining/estimating s, a general discussion will be provided withrespect to formulation of the cost function. Thereafter, the exampleprocesses of determining/estimating s will be described with referenceto FIGS. 5 and 6.

First, a formulation of a cost function (which may also be referred toas an optimization cost function) is described. Optimization costfunctions may be formulated in terms of analysis or synthesisregularization terms or a mixture thereof. Example embodiments hereinare only meant to describe some specific cases of the formulation ofsuch optimization cost functions and therefore, the choice of analysisor synthesis terms or a combination thereof presented herein, aredemonstrative and not meant to be limiting. Alternatively, anoptimization cost function may be formulated from a Bayesian estimationtheory perspective and estimate the desired signal (e.g. through themaximum a posteriori (MAP) estimate). Such alternative formulations ofthe cost function and the corresponding solutions may be derived bythose skilled in the art and example embodiments of the optimizationcost function formulation presented herein, are meant to bedemonstrative only and thus are not meant to be limiting.

In example embodiments, a cost function may be defined as J(s) shown inEquation (15) below, the solution to which provides an estimation of sdenoted by ŝ given y.

$\begin{matrix}{\hat{s} = {\underset{s}{argmin}\left\{ {{J(s)} = {{\frac{1}{2}{{y - {F_{D}^{H}\left( {h*_{r}s} \right)}}}_{2}^{2}} + {\phi \left( {\lambda \odot s} \right)}}} \right\}}} & (15)\end{matrix}$

where ½∥y−F_(D) ^(H)(h*_(r)s)∥₂ ² is the data fidelity term using theenergy metric, φ(z) is the regularization function (the determination ofwhich will be described below), λ is the regularization parameter, andthe remaining notations used in Equation (15) are as defined above.Furthermore, ŝ in Equation (15) may be considered to be one of possiblesets of values that minimize the cost function given by Equation (15).

Using Parseval's theorem, the convolution theorem, the commutativeproperty of the range and Doppler Fourier transforms and Equations(10)-(14), the cost function J(s) of Equation (15) may be rewritten asbelow:

$\begin{matrix}\begin{matrix}{{J(s)} = {{\frac{1}{2}{{F_{R}\left( {y - {F_{D}^{H}\left( {h*_{r}s} \right)}} \right)}}_{2}^{2}} + {\phi \left( {\lambda \odot s} \right)}}} \\{= {{\frac{1}{2}{{{F_{R}y} - {F_{R}{F_{D}^{H}\left( {h*_{r}s} \right)}}}}_{2}^{2}} + {\phi \left( {\lambda \odot s} \right)}}} \\{= {{\frac{1}{2}{{{F_{R}y} - {F_{D}^{H}{F_{R}\left( {h*_{r}s} \right)}}}}_{2}^{2}} + {\phi \left( {\lambda \odot s} \right)}}} \\{= {{\frac{1}{2}{{{F_{R}y} - {\sqrt{N_{r}}{F_{D}^{H}\left( {F_{R}h*_{r}F_{R}S} \right)}}}}_{2}^{2}} + {\phi \left( {\lambda \odot s} \right)}}} \\{= {{\frac{1}{2}{{Y - {\sqrt{N_{r}}{F_{D}^{H}\left( {H \odot_{R}S} \right)}}}}_{2}^{2}} + {\phi \left( {\lambda \odot s} \right)}}} \\{= {{\frac{1}{2}{{Y - {\sqrt{N_{r}}F_{D}^{H}{{rpm}(H)}S}}}_{2}^{2}} + {\phi \left( {\lambda \odot s} \right)}}} \\{{{\frac{1}{2}{{Y - {\sqrt{N_{r}}{{rpm}(H)}F_{D}^{H}S}}}_{2}^{2}} + {\phi \left( {\lambda \odot s} \right)}}}\end{matrix} & \begin{matrix}(16) \\\; \\(17) \\\; \\(18) \\\; \\(19) \\\; \\(20) \\\; \\(21) \\(22)\end{matrix}\end{matrix}$

where Y, H, and S are defined as the range Fourier transforms of y, hand s, as shown in Equation (23).

Y=F _(R) y,H=F _(R) h,S=F _(R) s,  (23)

Hence, Equation (15) may be rewritten as:

$\begin{matrix}{{\hat{s} = {{argmin}_{s}\left\{ {{J(s)} = {{\frac{1}{2}{{Y - {\sqrt{N_{r}}{{rpm}(H)}F_{D}^{H}S}}}_{2}^{2}} + {\phi \left( {\lambda \odot s} \right)}}} \right\}}},{{{where}\mspace{14mu} S} = {F_{R}s}}} & (24)\end{matrix}$

The solution to Equation (24) may be obtained by using the AlternatingDirection Method of Multipliers (ADMM). However, example embodiments arenot limited to using ADMM and other methods may be used instead,including but not limited to, dual decomposition method, the method ofmultipliers, Douglas-Rachford splitting, Spingarn's method of partialinverses, Dykstra's alternating projections, Bregman iterativealgorithms for l₁ problems, proximal methods, etc. Furthermore, othernumerical and sparsity optimization methods in solving Equation (24) maybe used.

Example advantages of ADMM include fast convergence, the use of fasttransforms such as the FFT, and potentially avoiding the need forperforming any matrix inversions or multiplications. In addition to thebasic ADMM algorithm, example embodiments may apply variations of theADMM, as is known in the art.

Using variable splitting, Equation (24) may be expressed as:

$\begin{matrix}{{\hat{s} = {\underset{s}{argmin}\left\{ {{J(s)} = {{\frac{1}{2}{{Y - {\sqrt{N_{r}\;}{{rpm}(H)}F_{D}^{H}S}}}_{2}^{2}} + {\phi \left( {\lambda \odot z} \right)}}} \right\}}}{{{such}\mspace{14mu} {that}\mspace{14mu} s} = {{z\mspace{14mu} {where}\mspace{14mu} S} = {F_{R}s}}}} & (25)\end{matrix}$

Using ADMM, the solution of Equation (25) may be obtained via a generalalgorithm given by:

$\begin{matrix}{\mspace{20mu} {z^{(j)} = {\underset{z}{argmin}\left\{ {{\phi \left( {\lambda \odot z} \right)} + {\frac{\mu}{2}{{s^{({j - 1})} - z - d^{({j - 2})}}}_{2}^{2}}} \right\}}}} & (26) \\{S^{(j)} = {{\underset{s}{argmin}\frac{1}{2}{{Y - {\sqrt{N_{r}}{{rpm}(H)}F_{D}^{H}S}}}_{2}^{2}} + {\frac{\mu}{2}{{{F_{R}^{H}S} - z^{(j)} - d^{({j - 1})}}}_{2}^{2}}}} & (27) \\{\mspace{20mu} {s^{(j)} = {F_{R}^{H}S^{(j)}}}} & (28) \\{\mspace{20mu} {d^{(j)} = {d^{({j - 1})} - \left( {s^{(j)} - z^{(j)}} \right)}}} & (29)\end{matrix}$

where μ and λ are the step-size (also called multipliers) andregularization parameters, respectively. The regularization parametermay be a scalar or a higher dimensional vector and μ may be adaptable ineach iteration. The variable d is an auxiliary ADMM variable used in theADMM algorithm, as is known in the art.

In Equation (26), optimization is performed over the variable z whilethe values of s and d are updated in each iteration of the iterativealgorithm. Similarly, in Equation (27), the optimization is performedover the variable S while using the new value obtained for z in Equation(26) and the value of d from the previous iteration. However in Equation(29), the update of the variable d is based on the new values obtainedfor s and z using d from the previous iteration.

In one example embodiment and in order to solve Equation (27), Equation(27) may be transformed into the Frequency domain using Equation (13).Accordingly, Equation (27) may be represented in the frequency domainas:

$\begin{matrix}{S = {{\underset{s}{argmin}\frac{1}{2}{{Y - {\sqrt{N_{r}}{{rpm}(H)}F_{D}^{H}S}}}_{2}^{2}} + {\frac{\mu}{2}{{S - Z - D}}_{2}^{2}}}} & (30)\end{matrix}$

where S, D, and Z are defined as the range Fourier transforms of s, zand d, respectively, as shown below.

S=F _(R) s,Z=F _(R) z,D=F _(R) d,  (31)

Equation (30) may be expressed as:

$\begin{matrix}{S = {{\underset{s}{argmin}\frac{1}{2}{{Y - {AS}}}_{2}^{2}} + {\frac{\mu}{2}{{S - B}}_{2}^{2}}}} & (32)\end{matrix}$

where

A=√{square root over (N _(r))} rpm(H)F _(D) ^(H) ,B=Z+D  (33)

The solution of Equation (32) (i.e., the radar signal to bedetermined/estimated from the received signal y) is given by:

S=(A ^(H) A+μI)⁻¹(A ^(H) Y+μB)  (34)

However, the operator A^(H)A is not diagonal because of Equation (4b),so determination of the inverse of (A^(H)A+μI)⁻¹ is computationallycomplex. Accordingly, the matrix inverse lemma may be used to simplifythe expression in Equation (34). The symbol “.l” is used to denoteelement-wise division and the symbol “.̂” is used to denote element wisemultiplication. Therefore, the inverse of (A^(H)A+μI)⁻¹ in Equation (34)may be written as:

$\begin{matrix}\begin{matrix}{\left( {{A^{H}A} + {\mu \; I}} \right)^{- 1} = {{\frac{1}{\mu}I} - {\frac{N_{r}}{\mu}F_{D}{{rpm}\left( H^{*} \right)}}}} \\{{\left( {{\mu \; I} + {N_{r}{{rpm}(H)}F_{D}^{H}F_{D}{{rpm}\left( H^{*} \right)}}} \right)^{- 1}{{rpm}(H)}F_{D}^{H}}} \\{= {{\frac{1}{\mu}I} - {\frac{N_{r}}{\mu}F_{D}{{rpm}\left( H^{*} \right)}}}} \\{{\left( {{\mu \; I} + {N_{r}{{rpm}(H)}{{rpm}\left( H^{*} \right)}}} \right)^{- 1}{{rpm}(H)}F_{D}^{H}}} \\{= {{\frac{1}{\mu}I} - {\frac{N_{r}}{\mu}F_{D}{{rpm}\left( H^{*} \right)}}}} \\{{\left( {{\mu \; I} + {N_{r}{{rpm}\left( {H}^{.{\bigwedge 2}} \right)}}} \right)^{- 1}{{rpm}(H)}F_{D}^{H}}} \\{= {{\frac{1}{\mu}I} - {\frac{N_{r}}{\mu}F_{D}{{rpm}\left( H^{*} \right)}\left( {{rpm}\left( {{N_{r}{H}^{.{\bigwedge 2}}} + \mu} \right)} \right)^{- 1}}}} \\{{{{rpm}(H)}F_{D}^{H}}} \\{= {{\frac{1}{\mu}I} - {\frac{N_{r}}{\mu}F_{D}{{rpm}\left( H^{*} \right)}{rpm}}}} \\{{\left( {1./\left( {{N_{r}{H}^{.{\bigwedge 2}}} + \mu} \right)} \right){{rpm}(H)}F_{D}^{H}}} \\{= {{\frac{1}{\mu}I} - {\frac{N_{r}}{\mu}F_{D}{{rpm}\left( {\left( {N_{r}{{{H}^{.{\bigwedge 2}}.}/\left( {{N_{r}{H}^{.{\bigwedge 2}}} + \mu} \right)}} \right)F_{D}^{H}} \right.}}}}\end{matrix} & \begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}(35) \\\;\end{matrix} \\\;\end{matrix} \\(36)\end{matrix} \\\;\end{matrix} \\\;\end{matrix} \\\left. (37) \right)\end{matrix} \\\; \\\; \\(38) \\\begin{matrix}\; \\\; \\\; \\(39) \\\begin{matrix}\; \\(40)\end{matrix}\end{matrix}\end{matrix}\end{matrix}$

A variable P may be defined as:

$\begin{matrix}{P = {1./\left( {1 + {{\left( \frac{\mu}{N_{r}} \right).}/{\frac{\mu}{N_{r}}}^{.{\bigwedge 2}}}} \right)}} & (41)\end{matrix}$

Accordingly, the solution of Equation (34) may be given by:

$\begin{matrix}\begin{matrix}{S = {\left( {{A^{H}A} + {\mu \; I}} \right)^{- 1}\left( {{A^{H}Y} + {\mu \; B}} \right)}} \\{= {\left( {{\frac{1}{\mu}I} - {\frac{1}{\mu}F_{D}{{rpm}(P)}F_{D}^{H}}} \right)\left( {{\sqrt{N_{r}}F_{D}{{rpm}\left( H^{*} \right)}Y} + {\mu \left( {Z + D} \right)}} \right)}} \\{= {\left( {I - {F_{D}{{rpm}(P)}F_{D}^{H}}} \right)\left( {{\frac{\sqrt{N_{r}}}{\mu}F_{D}{{rpm}\left( H^{*} \right)}Y} + Z + D} \right)}}\end{matrix} & \begin{matrix}\begin{matrix}\begin{matrix}(42) \\\;\end{matrix} \\\;\end{matrix} \\(43)\end{matrix}\end{matrix}$

In simplifying Equation (43), a new variable R may be defined as:

$\begin{matrix}{R = {{\frac{\sqrt{N_{r}}}{\mu}F_{D}{{rpm}\left( H^{*} \right)}Y} + Z + D}} & (44)\end{matrix}$

Then, Equation (43) may be rewritten as:

S=R−F _(D) rpm(P)F _(D) ^(H) R  (45)

In one example embodiment, the variable R may also be rewritten as givenbelow in Equation (46), which in turn may be used to rewrite Equation(45) as shown below in Equation (47).

$\begin{matrix}{R = {{\frac{\sqrt{N_{r}}}{\mu}{F_{D}\left( {H^{*} \odot_{R}Y} \right)}} + Z + D}} & (46) \\{S = {R - {F_{D}\left( {P \odot_{R}\left( {F_{D}^{H}R} \right)} \right)}}} & (47)\end{matrix}$

Next the determination of an appropriate regularization term isdescribed. The regularization function φ(z) in equation (26) may be areconfigurable function determined based on empirical studies ormathematical models. In one example embodiment, φ(z) is chosen to be afunction that allows for simultaneous operation of radar and wirelesscommunications systems. For example, the regularization function may bea combination of regularization functions with different regularizationparameter weights. Furthermore, the regularization function φ(z) may bea sparsity promoting function such as the l₁ norm, the nuclear norm,group sparse functions, non-convex penalties, total variation (in range,Doppler, PRI, CPI or scan, etc.), sparsity in a transform domain such aswavelets and Fourier domains, sparsity using prior knowledge such asclutter maps, mixed norms, the Huber function, non-pure sparsefunctions, compound functions, sparsity in time-frequency transformssuch as the short-time Fourier domain, etc., depending on the radarsignal being transmitted and the radar scene to be reconstructed.Accordingly, particular choice(s) for the regularization function usedin the present disclosure for the radar scenario in consideration, mayeasily be modified/replaced by other regularization functions that areknown or are to be developed for achieving simultaneous transmission ofradar and wireless communications systems based signals. Therefore,example embodiments are not limited to the specific choice(s) of theregularization function described herein.

Furthermore, while for purposes of describing example embodiments, anassumption is made that the data being regularized is in theDoppler-range domain, it is also possible to have the regularizationfunction promote sparsity, group-sparsity, nuclear norm, total variationetc. on other domains such as the range-pulse domain. For example, bysetting F_(D) ^(H)=F_(D)=I_(D), where I_(D) operates on each column ofthe data matrix by returning the same column, the terms F_(D) ^(H),F_(D) will no longer be included in Equations (15), (16) and thesolutions given in Equations (46) and (47). Accordingly, x will be thesame as s (i.e., x=s and therefore X=S) and Equation (27) is similarlysolved in the range-pulse domain. Therefore, the algorithmic frameworkprovided in example embodiments described herein is equally applicableto a penalty function set on multiple pulses in other domains such asthe range-pulse domain and range only domain. An example embodiment, inwhich the algorithm is applied without using Doppler information in therange only domain, will be described later below.

Using the concept of proximity operator, Equation (26) may be re-writtenas:

$\begin{matrix}{{{prox}_{\phi,\lambda,\mu}(b)} = {\underset{z}{argmin}\left\{ {{\phi \left( {\lambda \odot z} \right)} + {\frac{\mu}{2}{{b - z}}_{2}^{2}}} \right\}}} & (48)\end{matrix}$

While closed-form expressions of the proximity operators of variousfunctions exist in order to obtain a solution of Equation (48), ifclosed-form expressions are not derivable, example embodiments may applyother known or to be developed numerical optimization methods to obtainan estimate of the proximity operator in Equation (48).

As described above, example embodiments may utilize group-sparsity asthe regularization function φ(z) in Equation (48) (Equation (49)). Thepulse-range or Doppler-range data may have group sparsity. For example,an extended target may possess group range sparsity and a non-constantradar cross section (RCS) target may possess group Doppler sparsity.Example embodiments may use group-sparsity in Doppler-range although thesame may be used in other domains such as pulse-range domain.Accordingly, it is appropriate to define φ(z) so to reflect the domainpart.

In doing so, example embodiments utilize K_(D) and K_(R) to denote thenumber of Doppler bins and number of range bins respectively, to promoteDoppler-range group sparsity. The group-sparsity technique is meant asan exemplary model of a group-sparse regularization function. To promoteDoppler-range group sparsity, we define:

$\begin{matrix}{{\phi (z)} = {\sum\limits_{i}{\sum\limits_{n}{\psi \left( {{z\left( {{i + \left( {{0\text{:}K_{D}} - 1} \right)},{n + \left( {{0\text{:}K_{D}} - 1} \right)}} \right)}}_{2} \right)}}}} & (49)\end{matrix}$

The two dimensional array z(i+(0: K_(D)−1),n+(0:K_(R)−1)) is a sub-arrayof z of size K_(D)×K_(R). The first element of the sub-array is z(i, n).The penalty function ψ may be a convex or non-convex sparsity-promotingfunction, which may depend on one or more parameters as shown below inEquations (50)-(52).

$\begin{matrix}{{\psi (t)} = {t}} & (50) \\{{\psi \left( {t;a} \right)} = {{\frac{1}{a}{\log \left( {1 + {a{t}}} \right)}\mspace{20mu} {s.t.\; a}} > 0}} & (51) \\{{\psi \left( {t;a} \right)} = {{\frac{2}{a\sqrt{3}}\left( {{\tan^{- 1}\left( \frac{1 + {2a{t}}}{\sqrt{3}} \right)} - \frac{\pi}{6}} \right)\mspace{25mu} {s.t.\; a}} > 0}} & (52)\end{matrix}$

where Equations (51) and (52) are equal to Equation (50) (the L1 norm)when a=0. Equations (51)-(52) are examples of different penaltyfunctions that may be used. However, example embodiments are not limitedthereto and other known or to be developed sparsity promoting penaltyfunctions may be utilized instead. In one example embodiment, a penaltyfunction may be defined as a combination of penalty functions or aseparate penalty function for each of the Doppler and range groups maybe defined, with each overlapping or non-overlapping Doppler and rangegroups having different sizes.

Furthermore, for a>0, the sparsity promoting penalty functions definedby Equations (51) and (52) may promote a stronger sparsity than thesparsity promoting penalty function defined by Equation (50).Furthermore, the sparsity promoting penalty functions (51) and (52) maybe non-convex.

Both Equations (15) and (25) contain a convex data fidelity term. If anon-convex regularization function for solving Equations (15) andEquation (25) is used, it is still possible to make the total costfunction as convex by choosing a appropriately in Equations (51) and(52). For example, a may be selected such that the positive secondderivative in the data-fidelity term balances against the negativesecond derivative in the non-convex regularizer function.

In yet another example embodiment, choosing K_(R)=1 and K_(D)=1, andusing Equation (50), the l₁ norm may be obtained, which is applied oneach element of the matrix z as defined above, given by Equation (53)below.

$\begin{matrix}{{\phi (z)} = {\sum\limits_{i}\; {\sum\limits_{n}\; {{z\left( {i,n} \right)}}}}} & (53)\end{matrix}$

Using this regularization function, the proximity operator given inEquation (48) is the soft threshold function on each element of z.

The regularization parameter λ in Equation (15) may be a scalar or ahigher dimensional vector. For higher dimensional vectors, theregularization parameter may be applied element-wise for someregularization functions such as the l₁ norm and may be cast in a vectoror matrix form. For example, the regularization parameter may be amatrix λ for the l₁ norm and may be written as:

$\begin{matrix}{{\phi \left( {\lambda \; \odot \; z} \right)} = {\sum\limits_{i}\; {\sum\limits_{n}\; {{\lambda \left( {i,n} \right)}\; {{z\left( {i,n} \right)}}}}}} & (54)\end{matrix}$

where the proximity operator for such a case is soft-threshold appliedelement-wise with the threshold parameter being λ(i, n). Consequently,such extension of the regularization parameter is obvious to thoseskilled in the arts and the proximity operator defined in Equation (48)is meant to also cover cases when the regularization parameter may be anon-scalar parameter such as vector or matrix.

As discussed above, it may be possible that Equation (48) does not havea closed form solution for some regularization functions such asregularization functions given in Equations (49) and (50-52) when theDoppler-range group sizes are more than 1 element. In such case and inorder to obtain a solution to Equation (48) for the regularizationfunction of Equation (49), a pulse filtering convolution operator *_(d)is defined. The operator *_(d) has analogous properties to *_(r) but isapplied on the pulse dimension (i.e., on each column of the data matrixy). The pulse filtering convolution function may be given by:

$\begin{matrix}{g*_{D}{x{\sum\limits_{k}\; {{g(k)}{x\left( {{\langle{m - k}\rangle}_{N_{d}},l} \right)}}}}} & (55)\end{matrix}$

where x is in the range-pulse domain.

Appropriate zero-padding may be used in the pulse domain in a similarmanner as described above with respect to the range domain in order toconvert a linear convolution into a circular convolution. Consequently,the pulse filtering convolution may be implemented in Doppler Frequencydomain by point-wise multiplication, as shown below in equation (56):

F _(D)(g* _(D) x)=√{square root over (N _(D))}(F _(D) g⊙ _(D) F _(D)x)=√{square root over (N _(D))}G⊙ _(D) s  (56)

where G is the Doppler Fourier transform of the vector g, and s is theDoppler Fourier transform of x. In Equation (56) g and G areone-dimensional vectors while x and s are two-dimensional vectors.Hence, for point-wise multiplication to be defined, the one dimensionalvector is expanded to a two dimensional vector. Therefore, an operator⊙_(D) to expand the G vector so as to have equal number of columns as s,is provided by Equation (57) below.

G⊙ _(D) s

G(i)s(i,k)  (57)

A Majorization-Minimization (MM) algorithm may be used to solve Equation(48) for the regularization function given by Equation (49). TheMajorization-Minimization (MM) algorithm may allow for the elements ofthe group in Equation (49) to be weighted differently. In doing so,Doppler and Range kernals may be defined as:

p _(D) =[p _(D)(1), . . . ,p _(D)(K _(D))] with a length of K _(D)  (58)

p _(R) =[p _(R)(1), . . . ,p _(R)(K _(R))] with a length of K _(R)  (59)

where p_(D) and p_(R) may be conventional symmetric digital signalprocessing (DSP) windows such as the triangular or Hamming window.However, those skilled in the art appreciate that different weightingfunctions may be used for p_(D) and p_(R) instead of the conventionalDSP windows.

An iterative algorithm to solve Equation (48) for the regularizationfunction given by Equation (49) may be given by:

q=(p _(D)*_(D) p _(R)*_(R)(|z|.)^(.̂2))^(.̂1/2)  (60)

v=1+λ((p _(D)*_(D) p _(R)*_(R)1./θ(q))  (61)

z=b./v  (62)

where z is initialized to be equal to b and Equations (60)-(62) arerepeated until a convergence condition/criteria (which may be determinedbased on empirical studies) is satisfied. Furthermore, the operator |z|.on a vector or matrix is defined as taking the absolute value of eachelement z. In Equations (60)-(62), the operation designated by dot (.)denotes element-wise operation. Furthermore, the function θ is definedas:

$\begin{matrix}{{\theta (t)} = \frac{t}{\psi^{\prime}(t)}} & (63)\end{matrix}$

where ψ′(t) is derivative (whenever it is defined) of the penaltyfunction ψ(t) of the group of coefficients in the range-Doppler domain.In the example embodiment of the iterative algorithm described above,θ(q) is applied element-wise to each element of the array q. While theiterative algorithm of Equations (60)-(62) has not been solved in thefrequency domain, due to the expectation that the group sizes and thekernel weights have relatively small lengths, for large group sizes,Equation (61) and (62) may be solved in the range-frequency andDoppler-frequency domains.

Satisfying the convergence criteria may be detected by differentmethods. For example, satisfying the convergence criteria may beachieved by monitoring the change in z using an appropriate norm (forexample the Frobenius norm). Alternatively, a fixed number of iterationsmay be used as the convergence criteria. However, the convergencecriteria is not limited to the examples provided above and may includeany other convergence criteria.

As another example of a regularization function, a Doppler filter withinthe regularization function may be considered. The Doppler filter may beused to remove ground clutter for the purpose of moving targetindication (MTI) or conversely enhance near zero-Doppler targets byremoving fast moving targets. Accordingly, Equation (25) may berewritten as:

$\begin{matrix}{\hat{s} = {\underset{s}{argmin}\left\{ {{J(s)} = {{\frac{1}{2}{{Y - {\sqrt{N_{r}}{{rpm}(H)}F_{D}^{H}S}}}_{2}^{2}} + {\phi \left( {\lambda \odot G \odot_{D}s} \right)}}} \right\}}} & (64)\end{matrix}$

The effect of the regularization function φ(G⊙_(D) s) given in Equation(64) is that it enhances target detection if the targets are expected tobe outside of a particular Doppler band. For example, in one embodimentG may be zero (0) for some Doppler frequencies and one (1) for otherDoppler frequencies. Such regularization functions may be appropriatewhen the ground-clutter of the scene is not sparse but the objective ofthe radar is to detect a sparse number of targets whose Dopplerfrequency partially overlaps or does not overlap the ground clutterDoppler spectrum.

In one example embodiment, if the regularization function φ isconsidered the l₁ norm, the proximal operator in Equation (48) forφ(G⊙_(D) s) is given by:

$\begin{matrix}{{{z\left( {i,k} \right)} = {{{soft}\left( {{b\left( {i,k} \right)},{{{G(i)}}\frac{\lambda}{\mu}}} \right)}\mspace{14mu} {for}\mspace{14mu} {all}\mspace{14mu} i}},k} & (65)\end{matrix}$

where the soft-thresholding is applied element-wise.

Next, a modeling of the noise and interference is described. Asdescribed above, the noise/interference may be considered to includeboth the corresponding system noise (e.g., the corresponding wirelesscommunications system noise or the radar system noise) as well as theinterference signal 140, described above with reference to FIG. 1 and inEquation (1).

The noise of the radar system 120 at the receiver front-end may bemodelled as a white Gaussian noise. However, after receiver filtering,up sampling and other RF and signal processing processes, the noise maynot have a flat-spectrum. Furthermore, for simultaneous operation ofradar and wireless communications systems, the signal associated withthe wireless communications systems as seen by the radar system may bemodelled as colored noise/interference. Accordingly, the noise wconsists of the total noise process from both the radar receiver chainw_(n) (i.e., system noise) and the wireless interference w_(i) (i.e.,interference induced by the wireless communications system on radarsignals of the radar system) up to where the optimization algorithm isperformed. The power spectral density (PSD) of w may be denoted byP_(w). Since w depends on the RF frequency, the power spectral densityof the total noise process varies across the range-frequency. In oneexample embodiment, the length of P_(w) equals N_(r), which is thelength of the range-Fourier transform F_(R) (The range-Fourier transformis equivalent to the base-band frequencies of the signal for eachpulse). To account for this colored noise, the baseband frequencies ofthe data fidelity may be weighted as a function of P_(w). In one exampleembodiment, the square root of the reciprocal of P_(w) may be used asthe weight factor while use of other methods of weighting thefrequencies of the data fidelity term based on the power spectraldensity of the total noise (consisting of system noise and overlappinglytransmitted signals associated with a co-existing wirelesscommunications system), is apparent to those having ordinary skill inthe art. In one example embodiment, frequencies that do not correspondto a stationary process may be notched out by setting values of P_(w) toinfinity (e.g., in practice to a very large value). Using, thereciprocal of P_(w), Equation (25) may be modified as follows:

$\begin{matrix}{\hat{s} = {\underset{s}{argmin} \left\{ {{J(s)} = {{\frac{1}{2}\left. {{\left( {1./\sqrt{P_{w}}} \right) \odot_{R}\left( {Y - {\sqrt{N_{r}}{{rpm}(H)}F_{D}^{H}S}} \right._{2}^{2}} + {\phi \left( {\lambda \odot s} \right)}} \right\} {where}\mspace{14mu} S} = {F_{R}s}}} \right.}} & (66)\end{matrix}$

Equation (66) may be further simplified using Equations (7) and (8), asshown below:

$\begin{matrix}{\hat{s} = {\underset{s}{argmin}\left\{ {J = {{\frac{1}{2}{{{{rpm}\left( {1./\sqrt{P_{w}}} \right)}\left( {Y - {\sqrt{N_{r}}{{rpm}(H)}F_{D}^{H}S}} \right)}}_{2}^{2}} + {\phi \left( {\lambda \odot s} \right)}}} \right\}}} & (67) \\{= {{\underset{s}{argmin}\frac{1}{2}{{{{{rpm}\left( {1./\sqrt{P_{w}}} \right)}Y} - {\sqrt{N_{r}}{{rpm}\left( {1./\sqrt{P_{w}}} \right)}{{rpm}(H)}F_{D}^{H}S}}}_{2}^{2}} + {\phi \left( {\lambda \odot s} \right)}}} & (68) \\{= {{\underset{s}{argmin}\frac{1}{2}{{{\left( {1./\sqrt{P_{w}}} \right) \odot_{R}Y} - {\sqrt{N_{r}}{{rpm}\left( {{H.}/\sqrt{P_{w}}} \right)}F_{D}^{H}S}}}_{2}^{2}} + {\phi \left( {\lambda \odot s} \right)}}} & (69) \\{\mspace{79mu} {= {\underset{s}{argmin}\frac{1}{2}{{\left( {\overset{\sim}{Y} - {\sqrt{N_{r}}{{rpm}\left( \overset{\sim}{H} \right)}F_{D}^{H}S}} \right._{2}^{2} + {\phi \left( {\lambda \odot s} \right)}}}}}} & (70)\end{matrix}$

where

{tilde over (Y)}=(1./√{square root over (P _(w))})⊙_(R) Y,{tilde over(H)}=H./√{square root over (P _(w))}  (71)

Since the cost function of Equation (70) has the same form as the costfunction of Equation (25), the same optimization algorithm for thewhite-noise case may be used in the colored noise/interference case withthe change of variables indicated in Equation (71) for the colorednoise/interference case.

The interference coming from the wireless communications system into theradar band and seen by the radar receiver 122 maybe generally modelledas a colored stationary stochastic process (white noise being a specialcase of a colored stationary stochastic process). In one exampleembodiment, having a model of such interference from wirelesscommunications systems stored at the radar receiver 122, enables theradar receiver 122 to use the stored model to estimate the radar signalfrom the mixed interfered radar plus wireless communication signals.However, the model for the interference may not be available.Accordingly, the radar receiver 122 may over-estimate the power of thePSD, but may still allow for the recovery of the radar signal.

The PSD of the colored noise process from the wireless communicationscoming into the radar system may be obtained in several ways. Forexample, the radar receiver 122 may capture the second order statisticsof the wireless communications system, which includes the PSD. Standardtechniques to estimate the auto-correlation function from thetime-series samples of the wireless communications data may also be usedto obtain the PSD.

One example embodiment of obtaining the statistics of the interferenceinduced on the radar signals by the overlappingly transmitted signals ofthe wireless communications system is for the radar to extend the PRIinterval slightly and only use the fast-time samples obtained at the endof each return from a PRI when the scattering power from objects (e.g.,radar object of detection 126 shown in FIG. 1) have decreasedsufficiently (e.g., a margin below system operating noise level). Yet,another example embodiment of obtaining the interference statisticsinduced on the radar signals by the overlappingly transmitted signals ofthe wireless communications system is to estimate the in-band wirelesscommunications signals via measurements of transmit-free or“listen-only” samples that represent stationary in-band interferenceduring a transmit-free operation at specific intervals. However, if theinterference statistics varies per each azimuth interval of a scan, awhole scan dedicated to a listening mode may be used to obtain theauto-correlation function for each azimuth sector of the radar 124.

In yet another example embodiment, the radar receiver 122 may obtain thestatistics of the interference induced on the radar signals by theoverlappingly transmitted signals of the wireless communications system,by knowing the location and distance of each wireless communicationsdevice (e.g., the UE 134 and/or the wireless access node 132 in FIG. 1)and using an absolute sum of the transmit power density formula for eachdevice with a priori knowledge of the frequencies used for transmissionby the wireless communication devices. This may correspond to an upperbound on the power spectral density. Other methods to set an upper boundon the maximum power assumed in each frequency that is used for spectrumsharing are known to those skilled in the art and are within the scopeof the present application.

In yet another example embodiment, the radar receiver 122 may obtain thestatistics of the interference induced on the radar signals by theoverlappingly transmitted signals of the wireless communications system,by obtaining a priori knowledge of the frequencies used by wirelesscommunications devices in a certain geographic location and setting theupper-bound for the power spectral density associated with suchfrequencies. Also further coordination between wireless communicationssystem and the radar system may be performed to obtain the powerspectral density of the wireless communications interference.

While example embodiments have been described in which the colored noisePSD is used as a weight factor in the data-fidelity term in order toobtain the best estimate of the range-Doppler matrix s, the PSD weightfactor may be adapted on a sample by sample basis, pulse by pulse basisor multiple CPI basis rather than a single CPI. If the colored noise isstationary in a period less than a single PRI period, the maximum valueof each frequency from a set of power-spectral densities obtainedthrough an adaptive window may be selected as an upper-bound for thewhole set of PSD functions. Alternatively, an average power-spectraldensity over a set of PSDs may be determined. Accordingly, theadaptation period for the colored noise/interference may be designedinto the optimization algorithm as a matrix weight factor for thedata-fidelity term, as appreciated by those having ordinary skill in theart.

Having described the formulation of the cost function, the data fidelityterm, the regularization term and the system noise, hereinafter exampleembodiments for determining/estimating s will be provided.

FIG. 5 is a flowchart describing a method of determining a signal inpresence of interference induced by an overlappingly transmitted signalof a different technology, according to an example embodiment. Forpurposes of describing example embodiments, FIG. 5 will be described inconjunction with the radar receiver 122 of the first system 120 shown inFIG. 1. Furthermore, the functionalities of the radar receiver 122described with reference to FIG. 5, will be implemented by the processor350 of the radar receiver 122, when the processor 350 executes thecomputer-readable instructions stored on the storage medium 345 of theradar receiver 122.

At S500, the radar receiver 122 receives a signal y, as defined inEquation (1) above. The signal y may be a series of pulse/range sampleswith additive colored noise interference, which may also be referred toas slow-time/fast-time data matrix. Given that the signal y includes theunderlying radar signal as well as the system noise and noise induced bythe interference signal 140 described above with reference to FIG. 1,signal y may be referred to as a mixed signal. Furthermore, the radarreceiver 122 may retrieve a plurality of system parameters from a memoryof the radar receiver 122 (e.g., from the storage medium device 345described above with reference to FIG. 3). The plurality of systemparameters may be programmed and stored in the storage medium device345. The plurality of system parameters may include the range-frequencyspectrum (H) of a transmission pulse by the radar 124, a set ofnon-negative Doppler weights (G) as described above, and the PSD P_(w)that includes the interference and the system noise, as described above.

At S505, the radar receiver 122 determines a regularization functionφ(s), as described above.

At S510, the radar receiver 122 formulates a cost function describedabove with reference to Equation (25), with Y and H of Equation (25)being replaced with {tilde over (Y)} and {tilde over (H)}, respectively,as shown in Equation (72) below. The radar receiver 122 formulates thecost function based on the signal y, the regularization function φ(s),determined at S505, as well as a regularization parameter and astep-size parameter.

More specifically, the formulated cost function may be represented byEquation (72) shown below.

$\begin{matrix}{{\hat{s} = {\underset{s}{argmin}\left\{ {{J(s)} = {{\frac{1}{2}{{\overset{\sim}{Y} - {\sqrt{N_{r}}{{rpm}\left( \overset{\sim}{H} \right)}F_{D}^{H}S}}}_{2}^{2}} + {\phi \left( {\lambda \odot s} \right)}}} \right\}}}{where}\mspace{14mu} {S = {F_{R}s}}} & (72)\end{matrix}$

The setting of the regularization parameter λ may depend on systemparameters such as the noise variance of the system, the waveformfilters used and the auto-correlation function of the colored noise. Thevalue of the regularization parameter λ may also be different fordifferent regularization functions. One method of setting theregularization parameter λ is through empirical studies that may be usedfor different scenarios of spectrum overlap, relative power of thenon-overlapping spectrum portions, the waveform filter, etc.

Another method of setting the regularization parameter λ is a formulabased on system parameters. Another method of setting the regularizationparameter λ is to test several different values of the regularizationparameter λ and ascertain the optimal value of the regularizationparameter λ, from among the test values of the regularization parameterλ, and the solutions of the costs function by means of statisticaltests. For example, in wireless communications, the statistical test maybe the cyclic redundancy check (CRC) and soft/hard error correction codemetrics. In radar, the statistical test may be a function of thecorrelation between the transmit waveform and the estimated radar scene.Other statistical tests (e.g. generalized cross validation, thediscrepancy principle, the L-curve criterion, normalized cumulativeperiodogram), which are known to those skilled in the art, may also beused. Henceforth, the choice of the regularization parameter λ does notchange the form of the optimization function and those skilled in theart may use such methods to set the regularization parameter λ fordifferent radar and wireless spectrum sharing scenarios.

The ADMM algorithm, which may be used in solving the cost functionsformed at S510, will converge for any step-size parameter μ. However theconvergence rate may differ for different values of the step-size μ. Thestep-size parameter μ may be chosen based on empirical studies or as afunction of systems parameters (e.g. noise variance). Alternatively, thestep-size parameter μ may be chosen adaptively in each iteration of theADMM algorithm based on functions of the difference between variables indifferent iterations of the ADMM loop.

At S515, the radar receiver 122 determines/estimates a radar signal(first signal), represented by ŝ, as described above. In one exampleembodiment, the radar receiver 122 may determine/estimate ŝ by applyingan iterative process to find a solution to cost function represented byEquation (72) and hence determine/estimate ŝ. In one example embodiment,the radar receiver 122 applies the iterative process as described below.

The radar receiver 122 initializes a plurality of variables, one or moreof which may be auxiliary variables defined for purposes of implementingthe iterative process. For example, the radar receiver 122 sets thepositive step-size parameter μ determined as described above. Similarly,the radar receiver 122 may set the regularization parameter λ to thevalue of the regularization parameter λ determined as described above.Furthermore, the radar receiver 122 may initialize variables s⁰ and d⁰to zero.

Based on the initialized values, the radar receiver 122 may determinevariables {tilde over (Y)}, {tilde over (H)}, P and R₀, as shown below:

$\begin{matrix}{\overset{\sim}{Y} = {\left( {1./\sqrt{P_{w}}} \right) \odot_{R}\left( {F_{R}y} \right)}} & (73) \\{\overset{\sim}{H} = {{H.}/\sqrt{P_{w}}}} & (74) \\{P = {1./\left( {1 + {\left( \frac{\mu}{N_{r}} \right) \cdot {/{\overset{\sim}{H}}} \cdot^{\bigwedge 2}}} \right)}} & (75) \\{R_{0} = {\frac{\sqrt{N_{r}}}{\mu}{F_{D}\left( {{\overset{\sim}{H}}^{*} \odot_{R}\overset{\sim}{Y}} \right)}}} & (76)\end{matrix}$

Furthermore, the radar receiver may define an auxiliary variable “j” andinitialize j to 0. The variable j may indicate the number of iterationsof the iterative process. Furthermore, the radar receiver may determinea regularization function, which may be the l₁ norm.

Thereafter, for j varying between 0 up to a number of iterations where aconvergence criterion has been satisfied, the radar receiver 122, mayrepeat Equations (77)-(81). The convergence criteria may be as describedabove.

$\begin{matrix}{j = {j + 1}} & (77) \\{{{z^{(j)}\left( {i,k} \right)} = {{{soft}\left( {{{s^{({j - 1})}\left( {i,k} \right)} - {d^{({j - 1})}\left( {i,k} \right)}},{{{G(i)}}\frac{\lambda}{\mu}}} \right)}\; {\forall i}}},k} & (78) \\{R^{(j)} = {R_{0} + {F_{R}\left( {z^{(j)} + d^{({j - 1})}} \right)}}} & (79) \\{s^{(j)} = {F_{R}^{H}\left( {R^{(j)} - {F_{D}\left( {P \odot_{R}\left( {F_{D}^{H}R^{(j)}} \right)} \right)}} \right)}} & (80) \\{d^{(j)} = {d^{({j - 1})} - \left( {s^{(j)} - z^{(j)}} \right)}} & (81)\end{matrix}$

Upon the convergence criteria being met, the resulting s^((j)) atEquation (80) is the determined/estimated ŝ. The determined/estimated ŝmay have two properties when the l₁ norm regularization function isused. First, a majority of the values of ŝ are negligible in amplitude.Second, a minority of the values ŝ are relatively larger in amplitude,thus indicating the determined/estimated radar pulses (first signal).

In another example embodiment, the radar receiver 122 may recover theradar pulses without using the Doppler frequency. For example, the phaseof the oscillator of wireless communications devices may not besynchronized with that of the radar 124, or for some radar operations,even if the Doppler shifts are known, estimating the return for each PRIindependent of other PRIs in the presence of wireless communications maynot be possible. Accordingly, it is possible to recover multiple pulsereturns or portion of a pulse return that is contaminated without usingDoppler frequency information.

Upon determining/estimating the radar signal at S515, then at S520, theradar receiver 122 may process information associated with thedetermined radar signal. For example, the radar receiver 122 may analyzethe determined radar signal to detect objects corresponding to theunderlying purpose of the radar system, track/monitor variables/objectsof interest (e.g., speed of cars, airplanes, ships, etc.). However, theprocessing of the radar signal is not limited to the examples describedabove but may encompass any appropriate type of analysis of thedetermined/estimated radar signal in order to extract/study/monitorinformation included in or associated with the determined/estimatedradar signal.

Furthermore, while FIG. 5 has been described from the perspective of theradar system and the radar receiver thereof, FIG. 5 may be easilymodified to be implemented at a receiver of another co-existing system(e.g., the wireless communications system 130 of FIG. 1). Accordingly,in such instance, the receiver at a given component of the wirelesscommunications system 130 may determine/estimate the radar signal asdescribed above at S515 and then subtract the determined radar signalfrom the received signal in order to determine underlying wirelesscommunications signal.

Furthermore, when the process of FIG. 5 is applied at a receiver of awireless communications system, the processing of information at S520corresponds to processing of information associated with the determinedwireless communications signal and not the determined/estimated radarsignal.

FIG. 6 is a flowchart describing a method of determining a signal inpresence of interference induced by an overlappingly transmitted signalof a different technology, according to an example embodiment. Forpurposes of describing example embodiments, FIG. 6 will be described inconjunction with the radar receiver 122 of the first system 120 shown inFIG. 1. Furthermore, the functionalities of the radar receiver 122described with reference to FIG. 6, will be implemented by the processor350 of the radar receiver 122, when the processor 350 executes thecomputer-readable instructions stored on the storage medium 345 of theradar receiver 122.

At S600, the radar receiver 122 receives a signal y, as defined inEquation (1) above. In contrast to S500 of FIG. 5, at S600, the signal ymay be a sampled time series. Given that the signal y includes theunderlying radar signal as well as the system noise and noise induced bythe interference signal 140 described above with reference to FIG. 1,signal y may be referred to as a mixed signal.

Furthermore, the radar receiver 122 may retrieve a plurality of systemparameters from a memory of the radar receiver 122 (e.g., from thestorage medium device 345 described above with reference to FIG. 3). Theplurality of system parameters may be programmed and stored in thestorage medium device 345. The plurality of system parameters mayinclude the range-frequency spectrum (H) of a transmission pulse by theradar 124, a set of non-negative Doppler weights (G) as described above,and the PSD P_(w) that includes the interference and the system noise,as described above.

At S605, the radar receiver 122 determines a regularization functionφ(x), as described above.

At S610, the radar receiver 122 formulates a cost function as shownbelow with reference to Equation (83). The radar receiver 122 formulatesthe cost function based on the signal y, the regularization functionφ(s), determined at S605, as well as a regularization parameter and astep-size parameter.

$\begin{matrix}{\hat{x} = {\underset{x}{argmin}\left\{ {{\frac{1}{2}{{\overset{\sim}{Y} - {\sqrt{N_{r}}\left( {\overset{\sim}{H} \odot X} \right)}}}_{2}^{2}} + {\phi \left( {\lambda \odot X} \right)}} \right\}}} & (82)\end{matrix}$

where {tilde over (Y)} is the frequency transform of time-series ofsamples y, zero-padded appropriately to N_(r) in order to have thelinear convolution as a circular convolution.

The setting of the regularization parameter λ may depend on systemparameters such as the noise variance of the system, the waveformfilters used and the auto-correlation function of the colored noise. Thevalue of the regularization parameter λ may also be different fordifferent regularization functions. One method of setting theregularization parameter λ is through empirical studies that may be usedfor different scenarios of spectrum overlap, relative power of thenon-overlapping spectrum portions, the waveform filter, etc.

Another method of setting the regularization parameter λ is a formulabased on system parameters. Another method of setting the regularizationparameter λ is to test several different values of the regularizationparameter λ and ascertain the optimal value of the regularizationparameter λ, from among the test values of the regularization parameterλ, and the solutions of the costs function by means of statisticaltests. For example, in wireless communications, the statistical test maybe the cyclic redundancy check (CRC) and soft/hard error correction codemetrics. In radar, the statistical test may be a function of thecorrelation between the transmit waveform and the estimated radar scene.Other statistical tests (e.g. generalized cross validation, thediscrepancy principle, the L-curve criterion, normalized cumulativeperiodogram), which are known to those skilled in the art, may also beused. Henceforth, the choice of the regularization parameter λ does notchange the form of the optimization function and those skilled in theart may use such methods to set the regularization parameter λ fordifferent radar and wireless bandwidth sharing scenarios.

The ADMM algorithm, which will be used in solving the cost functionformed at S610, will converge for any step-size parameter μ. However theconvergence rate may differ for different values of the step-size μ. Thestep-size parameter μ may be chosen based on empirical studies or as afunction of systems parameters (e.g. noise variance). Alternatively, thestep-size parameter μ may be chosen adaptively in each iteration of theADMM algorithm based on functions of the difference between variables indifferent iterations of the ADMM loop.

At S615, the radar receiver 122 determines/estimates a radar signal(first signal). In one example embodiment, the radar receiver 122 mayapply an iterative process in order to determine/estimate {circumflexover (x)}. In one example embodiment, the radar receiver 122 applies theiterative process as described below.

The radar receiver 122 may determine variables {tilde over (Y)}, {tildeover (H)}, P and R, as shown below:

$\begin{matrix}{\overset{\sim}{Y} = {\left( {1./\sqrt{P_{w}}} \right) \odot ({Fy})}} & (83) \\{\overset{\sim}{H} = {{H.}/\sqrt{P_{w}}}} & (84) \\{P = {1./\left( {1 + {\left( \frac{\mu}{N_{r}} \right) \cdot {/{\overset{\sim}{H}}} \cdot^{\bigwedge 2}}} \right)}} & (85) \\{R = {\frac{\sqrt{N_{r}}}{\mu}\left( {{\overset{\sim}{H}}^{*} \odot \overset{\sim}{Y}} \right)}} & (86)\end{matrix}$

Furthermore, the radar receiver 122 may define an auxiliary variable “j”and initialize j to 0. The variable j may indicate the number ofiterations of the iterative process. Furthermore, the radar receiver maydetermine a regularization function, which may be the l₁ norm.

Thereafter, for j varying between 0 up to a number of iterations where aconvergence criterion has been satisfied, the radar receiver 122 mayrepeat Equations (87)-(91). The convergence criteria may be as describedabove.

$\begin{matrix}{j = {j + 1}} & (87) \\{v^{(j)} = {{{soft}\left( {{x^{({j - 1})} - d^{({j - 1})}},\frac{\lambda}{\mu}} \right)} + d^{({j - 1})}}} & (88) \\{X^{(j)} = {\left( {{Fv}^{(j)} + R} \right) \odot P}} & (89) \\{x^{(j)} = {F^{H}X^{(j)}}} & (90) \\{d^{(j)} = {v^{(j)} - x^{(j)}}} & (91)\end{matrix}$

Upon the convergence criteria being met, the resulting x^((j)) atEquation (91) is the determined/estimated {circumflex over (x)}. Thedetermined/estimated {circumflex over (x)} may have two properties whenthe l₁ norm regularization function is used. First, a majority of thevalues of {circumflex over (x)} are negligible in amplitude. Second, aminority of the values {circumflex over (x)} are relatively larger inamplitude, thus indicating the determined/estimated returned radarpulses.

Upon determining/estimating the radar signal at S615, then at S620, theradar receiver 122 may process information associated with thedetermined radar signal. For example, the radar receiver 122 may analyzethe determined radar signal to detect objects corresponding to theunderlying purpose of the radar system, track/monitor variables/objectsof interest (e.g., speed of cars, airplanes, ships, etc.). However, theprocessing of the radar signal is not limited to the examples describedabove but may encompass any appropriate type of analysis of thedetermined/estimated radar signal in order to extract/study/monitorinformation included in or associated with the determined/estimatedradar signal.

Furthermore, while FIG. 6 has been described from the perspective of theradar system and the radar receiver thereof, FIG. 6 may be easilymodified to be implemented at a receiver of another co-existing system(e.g., the wireless communications system 130 of FIG. 1). Accordingly,in such instance, the receiver at a given component of the wirelesscommunications system 130 may determine/estimate the radar signal asdescribed above at S615 and then subtract the determined radar signalfrom the received signal in order to determine underlying wirelesscommunications signal.

Furthermore, when the process of FIG. 6 is applied at a receiver of awireless communications system, the processing of information at S620will correspond to processing of information associated with thedetermined wireless communications signal and not thedetermined/estimated radar signal.

The processing of information associated with the determined signal atS520 and S620 depends on the underlying system at which the processesdescribed in FIG. 5 and/or FIG. 6 are implemented.

While FIGS. 5 and 6 are described above with reference to the radarreceiver 122, example embodiments are not limited thereto. For examplethe methods described above with reference to FIGS. 5 and 6, may beimplemented at a receiver in any one of the system components of awireless communications system such as the second system 130 shown inFIG. 1 (e.g., a receiver of any one of the UEs 134, the receiver of thewireless access node 132, etc.). Accordingly and as described above,such receiver at a component of the second system 130 may determineinterfering signal(s) (e.g., the interfering radar signal) in a similarmanner as described in example embodiments above and thereafter subtractthe determine signal(s) (combination of the determined radar signals incase of having more than one interfering radar signal) from the receivedsignal, in order to determine the wireless communications signal (e.g.,signal 136 as described above with reference to FIG. 1, and processinformation associated with the determined wireless communicationssignal.

In some example embodiments, there may be more than one system of aparticular technology. For example, in the setting shown in FIG. 1,there may be more than one radar system such as the system 120. In otherwords, there may be two radar systems 120 and the wirelesscommunications system 130 whose signals may be simultaneously andoverlappingly transmitted. Accordingly, a radar receiver 122 of any ofthe radar systems 120 may suppress the radar signals of the other one ofthe radar systems 120 (i.e., undesired radar signal) when implementingexample embodiments for determining/estimating the corresponding radarsignal (i.e., the desired radar signal). In this context, suppressing ofa radar signal may be understood to include eliminating the influence ofthe undesired radar signal sufficiently so that the undesired radarsignal induces minimal detrimental effect on determining/estimating thedesired radar signal.

In one example embodiment, any of the radar systems 120 may suppress theundesired radar signals of the other radar system(s) 120 by adjustingpower spectral densities in the cost function on frequencies on whichthe undesired radar signals of the other radar system(s) 120 aretransmitted.

In one example embodiment, there may be more than one wirelesscommunications system and a radar system. Accordingly, a receiver at acomponent of any of the wireless communications systems may suppress thesignals associated with the other wireless communications system(s)(i.e., the undesired wireless communications signals), when determiningthe radar signal and subsequently the intended wireless communicationssignal.

In one example embodiment, the receiver at a component of any of thewireless communications systems may suppress the undesired wirelesscommunications signals in a similar manner as described above withreference to the radar systems (e.g., adjusting power spectral densitiesin the cost function on frequencies on which the undesired wirelesscommunications signals are transmitted).

In another example embodiment and when the undesired wirelesscommunications signals are sparse, the receiver at a component of any ofthe wireless communications systems may suppress the undesired wirelesscommunications signals by subtracting the sparse undesired wirelesscommunications signals from the intended (desired wirelesscommunications) signal.

Example embodiments described above provide numerous advantages overexisting methods in the art, as described in the Background Section.Some of the example advantages are described below. The exampleadvantages are described with respect to one or more of exampleembodiments described herein. However, example advantages are not meantto limit all example embodiments described herein. One or more exampleembodiments may provide advantages other than the example advantagesdescribed below.

One example advantage over the DSA and DFS technology, described in theBackground Section, is that example embodiments allow for both types ofsystems to operate simultaneously, that is, the signals of the twodifferent systems (e.g., wireless communications and radar systems)overlap in the time domain while overlapping partially or fully infrequency domain.

Another example advantage is that example embodiments allow for theradar and wireless communications systems to be minimally coordinated.The only coordination may be related to the radar transmission waveformin a setting of a simultaneous operation of the two systems. The radartransmission waveform may also be measured in both the radar andwireless communications system without coordination. While exchange ofmore information between the radar and wireless communications systemsmay improve performance of both systems in a simultaneous operation,doing so according to example embodiments, is not necessary.

Variations of the example embodiments are not to be regarded as adeparture from the spirit and scope of the example embodiments, and allsuch variations as would be apparent to one skilled in the art areintended to be included within the scope of this disclosure.

What is claimed is:
 1. A device comprising: a memory configured to storecomputer-readable instructions therein; and a processor configured toexecute the computer-readable instructions to, receive a signalincluding at least a first signal operating based on a first technologyand a second signal operating based on a second technology, the secondsignal having been transmitted simultaneously with the first signal overthe same frequency and time domains for reception by the device, form acost function based on at least the received signal, a parameterassociated with the first signal and a power spectral density of thesecond signal, determine the first signal from the signal based on theformed cost function, and determine the second signal based on thesignal and the first signal for processing of information associatedwith the second signal.
 2. The device of claim 1, wherein the firstsignal is transmitted by a first system operating based on the firsttechnology and the second signal is transmitted by a second systemoperating based on the second technology.
 3. The device of claim 2,wherein the first signal and the second signal are transmitted withoutany coordination between the first system and the second system.
 4. Thedevice of claim 2, wherein the first system is a radar system and thefirst technology is a radar technology, the second system is a wirelesscommunication system and the second technology is a wireless accesstechnology, the device is a receiver of the wireless communicationssystem, the first signal is a radar signal transmitted by a transmitterof the radar system, and the second signal is a signal transmitted by atransmitter of the wireless communications system.
 5. The device ofclaim 1, wherein the first signal and the second signal overlapspatially.
 6. The device of claim 1, wherein the signal includes thefirst signal with additive noise corresponding to at least the secondsignal, and the processor is further configured to, minimize the costfunction associated with the received signal, and determine the firstsignal as possible values of the first signal that minimize the costfunction.
 7. The device of claim 1, wherein the first signal is a radarfast-time/slow-time data matrix.
 8. The device of claim 7, wherein theparameter is a range-frequency spectrum associated with a transmissionof the first signal, and the processor is configured to form the costfunction based on the range-frequency spectrum associated with thetransmission of the first signal, a set of Doppler weights, at least oneregularization function, at least one data-fidelity term, at least oneregularization parameter, a step-size parameter and the power spectraldensity of the second signal.
 9. The device of claim 1, wherein thefirst signal is a radar data time-series.
 10. The device of claim 9,wherein the parameter is a frequency response of a filter associatedwith a transmission of the first signal, and the processor is configuredto form the cost function based on at least the received signal, thefrequency response of the filter associated with the transmission of thefirst signal, a regularization parameter, at least one regularizationfunction, at least one data-fidelity term, at least one regularizationparameter a step-size parameter and the power spectral density of thesecond signal.
 11. A method comprising: receiving, at a device, a signalincluding at least a first signal operating based on a first technologyand a second signal operating based on a second technology, the secondsignal having been transmitted simultaneously with the first signal overthe same frequency and time domains for reception by the device;forming, at the device, a cost function based on at least the receivedsignal, a parameter associated with the first signal and a powerspectral density of the second signal; determining, at the device, thefirst signal from the signal based on the formed cost function; anddetermining, at the device, the second signal based on the signal andthe first signal for processing of information associated with thesecond signal.
 12. The method of claim 11, wherein the first signal istransmitted by a first system operating based on the first technologyand the second signal is transmitted by a second system operating basedon the second technology.
 13. The method of claim 12, wherein the firstsignal and the second signal are transmitted without any coordinationbetween the first system and the second system.
 14. The method of claim12, wherein the first system is a radar system and the first technologyis a radar technology, the second system is a wireless communicationsystem and the second technology is a wireless access technology, thedevice is a receiver of the wireless communications system, the firstsignal is a radar signal transmitted by a transmitter of the radarsystem, and the second signal is a signal transmitted by a transmitterof the wireless communications system.
 15. The method of claim 11,wherein the first signal and the second signal overlap spatially. 16.The method of claim 11, wherein the signal includes the first signalwith additive noise corresponding to at least the second signal, and themethod further comprises: minimizing the cost function associated withthe received signal, and determining the first signal as possible valuesof the first signal that minimize the cost function.
 17. The method ofclaim 11, wherein the first signal is a radar fast-time/slow-time datamatrix.
 18. The method of claim 17, wherein the parameter is arange-frequency spectrum associated with a transmission of the firstsignal, and the forming forms the cost function based on therange-frequency spectrum associated with the transmission of the firstsignal, a set of Doppler weights, at least one regularization function,at least one data-fidelity term, at least one regularization parameter,a step-size parameter and the power spectral density of the secondsignal.
 19. The method of claim 11, wherein the first signal is a radardata time-series.
 20. The method of claim 19, wherein the parameter is afrequency response of a filter associated with a transmission of thefirst signal, and the forming forms the cost function based on at leastthe received signal, the frequency response of the filter associatedwith the transmission of the first signal, a regularization parameter,at least one regularization function, at least one data-fidelity term,at least one regularization parameter a step-size parameter and thepower spectral density of the second signal.